What is the solution set for the inequation lx+1/x l>2?

Q. What is the solution set for the inequation |x+1/x |>2?

First of all from the question you’ve written it is not clear if |x+1/x | means

Anyway we’ll discuss both of them.

1.

Note that inside the modulus we are simply adding a number to its inverse. Sum of any positive number and its multiplicative inverse is always greater than 2 unless that number is 2. This can be proved by AM GM. Also if the inequality is true for any positive k then it is also true for –k as well.

Hence solution set will be R – {–1. 1}.

2.

Let **. **So the inequality becomes

**For t > –1:**

**For t < –1:**–1 –

*t*> 2

Hence,

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